الفهرس 
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Abstract
The Inverted Pendulum (IP) system is considered one of the most complex
systems in control theory. The inherited instabilities require applying permanent controllers in order to stabilize the cart position and swinging up the pendulum angle. IP system is non-linear, under actuated, unstable and non minimum phase system. The stable point cannot be obtained without applying permanent controllers to the system in order to make the pendulum in the desired position. That means external force shall be applied to the system in order to make the system in balance state. IP system is Single Input MultiOutput (SIMO) system. The input is represented by the external force that is
applied to the vehicle while the outputs are represented by the position of the vehicle and the angle of the pendulum. Modeling of a non linear system is introduced in this research work. The objective of the proposed techniques is to
balance the IP system with optimal output response performance for the two outputs.
In this research work, Variable Structure Adaptive Fuzzy (VSAF) with feedforward gain and Reduced Linear Quadratic Regulator (RLQR) are used to
stabilizing the vehicle position and swinging up the pendulum angle. VSAF is responsible for stabilizing the cart position while RLQR is used to swinging up the pendulum angle. The dynamics of the system are enhanced via feedforward gain. VSAF has many advantages over than classic Fuzzy Logic Controller (FLC). One of the main advantages is that the rules in proposed controllers are adaptive and not fixed like FLC. This saves effort and time to obtain the best performance for the output response. RLQR is responsible to the swinging up the pendulum angle. RLQR reduced the number of parameters required to obtain the gain for swinging up the pendulum. The parameters of
each controller, in addition to the feed-forward gain, are obtained using the optimization technique. Three optimization techniques are utilized in order to tune the parameters of the controllers. The first optimization technique is a hybrid technique between GWO and PSO techniques with fixed constants. The second optimization technique is a hybrid technique between GWO and PSO
techniques with adaptive constants. The third optimization technique is Harris Hawks Optimizer (HHO). The results showed that the GWO/PSO-AC and
HHO techniques succeeded in balancing the system efficiently with different
robustness tests. The obtained results are promising for applications in nuclear fields.